Intersection of Sets
Pronunciation: /ˌɪn tərˈsɛk ʃən/ ?
 Figure 1: Intersection. Click on the image to see a representation of A ∩ B. 

An intersection of two or more
sets
is a set containing the members that are in all of the sets. This is spoken, "Set
C is the intersection of sets
A and B."
This is written, C = A ∩ B.
Properties of Intersection of Sets
Property  Math Statement  Description 
Commutative  A ∩ B = B ∩ A  The intersection of sets is commutative 
Associative  (D ∩ E) ∩ F = D ∩ (E ∩ F)  The intersection of sets is associative 
Distributive  (D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F) (D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)  The intersection and union of sets are distributive 
Table 1: Properties of the intersection of two sets. 

References
 intersection. merriamwebster.com. Encyclopedia Britannica. (Accessed: 20100223). http://www.merriamwebster.com/dictionary/intersection.
 Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior, 3rd edition, pg 63. Princeton University Press, 1953. (Accessed: 20100223). http://www.archive.org/stream/theoryofgamesand030098mbp#page/n84/mode/1up.
 Goldrei, D.C.. Classic Set Theory: For Guided Independent Study, pg 4. Chapman & Hall Mathematics, July 1, 1996.
 Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra, 6th edition, pg 4. Thomson, Brooks/Cole, 2005.
More Information
 McAdams, David. Sets. lifeisastoryproblem.com. Life is a Story Problem LLC. 20090312. http://www.lifeisastoryproblem.com/algebra/sets.html.
 McAdams, David. Set. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 20091215. http://www.allmathwords.org/article.aspx?lang=en&id=Set.
Printed Resources
Cite this article as:
Intersection of Sets. 20100223. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/intersection.html.
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Revision History
20100223: Added "References" (
McAdams, David.)
20080607: Corrected spelling (
McAdams, David.)
20080328: Added properties (
McAdams, David.)
20070801: Initial version (
McAdams, David.)